Math Problem Statement

Determine whether the system of equations shown in the graph has no solution or infinitely many solutions. The two lines are ______, so the system of equations has ______.

Solution

The question is asking whether the system of equations shown in the graph has no solution or infinitely many solutions.

Looking at the image:

  • The two lines appear to be parallel. This is indicated by the fact that they never intersect.
  • For a system of linear equations, if two lines are parallel, they have the same slope but different y-intercepts, meaning they will never intersect.
  • A system with parallel lines has no solution because there is no point that satisfies both equations simultaneously.

So, the correct answers are:

  1. The two lines are parallel.
  2. The system of equations has no solution.

Would you like more details or have any questions?

Here are some related questions:

  1. What does it mean when two lines have infinitely many solutions?
  2. How can you tell if two lines are parallel just by looking at their equations?
  3. What is the slope-intercept form of a linear equation, and how does it help in identifying parallel lines?
  4. What types of systems of equations have exactly one solution?
  5. Can non-linear systems of equations also have no solution?

Tip: Remember, parallel lines always have the same slope but different y-intercepts.

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Math Problem Analysis

Mathematical Concepts

Linear Systems
Parallel Lines

Formulas

Slope formula
Equation of a line

Theorems

If two lines are parallel, they have no solutions.

Suitable Grade Level

Grade 8-10